# Which number is not a perfect square a.5,329 b.1,280 c.3,600 d.729?

Jul 5, 2015

$1280$ is not a square.

#### Explanation:

Of course you could use your calculator to find out, but in this case it can be done faster.

A square can never end in an odd number of zeroes. A zero at the end points to a factor $10 \mathmr{and} 2 \cdot 5$. In a square all factors are paired, so there should be an even number of zeroes.

BTW: this does not mean that every number ending in two zeroes is a square!

Jul 5, 2015

b. $1280$ is not a perfect square.

#### Explanation:

a. $5329 = {73}^{2}$
b. $1280 = {2}^{8} \cdot 5 = {\left({2}^{4}\right)}^{2} \cdot 5 = {16}^{2} \cdot 5$
c. $3600 = {2}^{4} \cdot {3}^{2} \cdot {5}^{2} = {\left({2}^{2} \cdot 3 \cdot 5\right)}^{2} = {60}^{2}$
d. $729 = {3}^{6} = {\left({3}^{3}\right)}^{2} = {27}^{2}$